Hourglass worm gear

ABSTRACT

The improved hourglass worm gear which has been produced by grinding a blank for the worm gear by rotating a grinding wheel about a grinding wheel shaft A while turning the grinding wheel shaft A about a tool shaft A3 which extends in parallel with a wheel shaft A2 perpendicular to a worm shaft A1 is characterized in that a cross-sectional shape of the grinding wheel taken in a plane inclusive of the grinding wheel shaft A exhibits a circular arc. 
     Since the cross-sectional shape of the grinding wheel for successively grinding a series of gear tooth surfaces on the hourglass worm gear is contoured in the form of a circular arc, the hourglass worm gear assures that a radius r of the circular arc has an increased degree of freedom and an ideal contact pattern can be obtained by properly adjusting the radius r. 
     A contour of each gear tooth shape having few variation of gear tooth engagement is determined by correctly adjusting the radius r of the circular arc as well as various conditions associated with correct generation of a series of gear tooth surfaces on the worm gear in order to assure the ideal contact pattern regardless of displacement of shafts as well as displacement of each gear tooth under a large magnitude of load.

This application is a divisional of copending application Ser. No.07/933,206, filed on Aug. 21, 1992, which is a continuation-in-part ofnow U.S. Pat. No. 5,235,786 copending application Ser. No. 07/608,469,filed on Nov. 2, 1991 now abandoned the entire contents of which arehereby incorporated by reference.

FIELD OF THE INVENTION AND RELATED ART STATEMENT

The present invention relates generally to an hourglass worm gearadapted to mesh with a worm wheel. More particularly, the presentinvention relates to an hourglass worm gear preferably employable for aworm type reduction gear or the like speed changing unit.

A method of producing a prior hourglass worm gear adapted to mesh with aworm wheel has been disclosed in an official gazette of JapanesePublication Patent NO. 19970/ 1987.

An outline of this prior invention will briefly be described below withreference to FIG. 10.

In the drawing, reference numeral I designates a worm shaft, referencenumeral II designates a wheel shaft and reference numeral III designatesa shaft of an intermediate gear operable for producing an hourglass wormgear. In addition, an absolute coordinate having a space held immovableis represented by 0-xyz in a right-hand ortho-gonal coordinate systemwherein an x-coordinate orients in the direction of the worm shaft I, az-coordinate orients in the direction of the wheel shaft II and ay-coordinate orients in the direction of a common perpendicular line tothe shafts I and II extending through points 0₁ and 0₂. As is apparentfrom the FIG. 10, the intermediate gear shaft III intersects the commonperpendicular line 0₂ 0₁ at a point 0₃ at a right angle but slantwiseextends through the point 0₃ by an angle α relative to the wheel shaftII. It should be noted that the point 0₁ is an intersection where theworm shaft I intersects the common perpendicular line 0₂ 0₁ and thepoint 0₂ is an intersection where the wheel shaft II intersects thesame. When it is assumed that a rotational speed of the worm shaft I isrepresented ω₁, a rotational speed of the wheel shaft II is representedby ω₂, a rotational speed of the intermediate gear shaft III isrepresented by ω₃, a translational speed of the intermediate gear in thedirection along the intermediate gear shaft III is represented by v₃,two rotational speed ratios are represented by i=ω₁ /ω₂, j=ω₁ /ω₃, apitch of screw movement of the intermediate gear is represented by h=v₃/ω₃, a distance between the two points 0₂ and 0₁ is represented by e anda distance between the two points 0₃ and 0₁ is represented by e₁, thefollowing three equations are established in accordance with anintermediate gear theory.

    e.sub.1 =e cos.sup.2 α                               (1)

    j=i cosα-sinα                                  (2)

    h=v.sub.3 /ω.sub.3 =e sinα·cosα (3)

To the contrary, in a case where a gear cutting tool having a suitableconfiguration is mounted on the intermediate gear shaft III whichsatisfies the foregoing equations (1) to (3) so that a gear cuttingoperation is performed for a blank for a worm gear mounted on the wormshaft I and a blank for a worm wheel mounted on the wheel shaft II, theworm gear comes in contact with the worm wheel with the same contactline therebetween (hereinafter referred to as a first contact line) as acontact line between the intermediate gear and the worm gear. Thismethod of generating a worm gear and a worm wheel has been heretoforereferred to as an indirect generating method.

Especially, in a case where the angle α is zero, the intermediate gearshaft III coincides with the wheel shaft II and in a case where theangle α is 90°, the intermediate gear shaft III coincides with the wormshaft I. In either case, therefore, it is not substantially requiredthat the presence of the intermediate gear is taken into account. Thus,in these cases, this method of generating a worm and a worm wheel hasbeen heretofore referred to as a direct generating method.

In addition, according to the "twice contact theory", in a case where aworm wheel is directly generated by using a tool of which configurationis coincident to the configuration of the worm gear which has beengenerated by using the intermediate gear which satisfies the conditionsrepresented by the aforementioned equations (1) to (3) or partiallycoincident to the same, the worm wheel is brought in contact with theworm wheel at a twice contact line as shown in FIGS. 7(A) and 7(B), T₂(hereinafter referred to as a second contact line) in addition to thesimultaneous contact at a first contact line T₁. It should be noted thata relative radius of curvature becomes infinitely large at the locationwhere the worm gear is just once brought in contact with the worm wheel.In practice, it is required that the line along which it can be expectedthat the relative radius of curvature becomes infinitely large islocated within the range where the worm gear meshes with the worm wheel.To meet the requirement, there unavoidably arises a problem as to howthe shape to be assumed by each gear tooth on the intermediate gear isdetermined.

According to the method as disclosed in an official gazette of JapanesePublication Patent NO. 19970/1987, a conical surface ( which may includea flat surface in a special case) is employed as a gear tooth surfacefor the intermediate gear.

FIG. 7(A) schematically illustrates an hourglass worm gear produced inaccordance with the method which has been disclosed in an officialgazette of Japanese Publication Patent NO. 19970/1987 and FIG. 7(B)schematically illustrates a worm wheel to mesh with the hourglass wormgear shown in FIG. 7 (A).

According to the prior invention, the hourglass worm gear has aplurality of contact lines as shown in FIG. 7(A), and the ineffectivegear tooth surface represented by hatching lines extends to the regionin the vicinity of the central part of the worm gear tooth.

On the other hand, a worm wheel which is to mesh with the hourglass wormgear produced in accordance with the prior invention has a plurality ofcurves each defined by a series of points on limitative normal lines, asshown in FIG. 7(B). With this worm wheel, the simultaneous contact linesand the direction of a relative speed define a small angle τ with theresult that a film of lubricant is insufficiently formed on each of thegear tooth surfaces.

A grinding wheel for grinding gear tooth surfaces on the hourglass wormgear is contoured in the conical shape as shown in FIG. 8 and FIG. 9,and a cross-sectional shape of the grinding wheel taken along a shaftthereof is composed of straight lines. In a case where a grindingoperation is performed as shown in FIG. 8, the generation line of theconical shape is used as a grinding wheel surface. On the other hand, ina case where a grinding operation is performed as shown in FIG. 9, thebottom surface of the conical shape is used as a grinding wheel surface.

In FIG. 8 and FIG. 9, reference numeral 01 designates a blank for thehourglass worm gear, reference numeral 02 designates a conical grindingwheel, reference numeral 03 designates a motor for rotationally drivingthe grinding wheel 02 and reference numeral 04 designates anotherconical grinding wheel of which a bottom surface is used as a grindingwheel surface.

The conventional hourglass worm gear as constructed and generated in theabove-described manner has been found to have the following problems.

(1) A pressure prevailing over the contact surface of a gear tooth and athickness of the lubricant film both of which have a substantial effecton a performance of the hourglass worm gear are largely governed bythree parameters, i. e. , (1) a length of each simultaneous contactline, (2) a relative radius of curvature at each contact point and (3)an angle defined by the simultaneous contact line and the direction of arelative speed.

(2) According to the prior invention, the hourglass worm gear does nothave any degree of freedom on the configuration to be assumed by agrinding wheel for generating a gear tooth shape. This makes itdifficult to attain modification and improvement in consideration of theaforementioned parameters (1) to (3).

(3) When the conventional hourglass worm gear receives a large load, acontact pattern of the hourglass worm gear having an unstable lead andan unstable pressure angle on the gear tooth surface thereof isdeteriorated due to an adverse influence induced by displacement of theworm shaft attributable to deformation of bearings, resulting in its ownexcellent properties (high efficiency and high load bearing ability)failing to be exhibited satisfactorily.

(4) Consequently, the present general status of the conventionalhourglass worm gear is such that a case hardening steel is employed as amaterial for the worm gear and a material having a high property ofwell-fitting to the opponent gear tooth surface on the worm gear buthaving a low strength (e.g., JIS PBC2, A1BC2 or the like each having ahardness ranging from about 100 to 150 H_(B)) is employed as a materialfor the worm wheel. This leads to the result that the hourglass wormgear has a low load bearing ability.

(5) An engineering plastic material be used as a material available forthe worm gear.

OBJECTS AND SUMMARY OF THE INVENTION

The present invention has been made with the foregoing background inmind.

Therefore, an object of the present invention is to provide an hourglassworm gear which has a small ineffective gear tooth surface region aswell as a method of producing the same.

Other object of the present invention is to provide a hourglass wormgear of which an effective gear engagement range is substantiallyenlarged and of which load bearing ability is substantially improved aswell as a method of producing the same.

Another object of the present invention is to provide an hourglass wormgear which assures that an angle defined by simultaneous contact linesand the direction of a relative speed can be enlarged and a thickness oflubricant film can be increased as well as a method of producing thesame.

Further another object of the present invention is to provide anhourglass worm gear for which a material having excellent mechanicalproperties and a high strength can be used as well as a method ofproducing the same.

To accomplish the above objects, the present invention provides anhourglass worm gear adapted to mesh with a worm wheel, wherein a torustype grinding wheel is substituted for the conventional conical typegrinding wheel which has been used for practicing an method of producinga hourglass worm gear adapted to mesh with a worm wheel as disclosed inan official gazette of Japanese Publication Patent NO. 19970/1987.

More specifically, the present invention provides a hourglass worm gearadapted to mesh with an worm wheel, a series of gear tooth surfaces onthe hourglass worm gear being generated by grinding a blank for the wormgear by rotating a grinding wheel about a grinding wheel shaft A at ahigh speed while turning the grinding wheel shaft A about a tool shaftA3 in parallel with a wheel shaft A2 extending perpendicular to a wormshaft A1, wherein a shape of a sectional plane inclusive of the grindingwheel shaft A of the grinding wheel exhibits a circular arc.

With the hourglass worm gear of the present invention, since the shapeof the grinding wheel for grinding a series of gear tooth surfaces onthe hourglass worm gear is contoured to assume a circular arc, a radiusr of the circular arc of the grinding wheel has an increased degree offreedom and an ideal contact pattern can be obtained by properlyadjusting the radius r of the circular arc.

A series of gear tooth surfaces on the hourglass worm gear which havefew variation of gear tooth engagement can be generated by properlyadjusting the radius r of the circular arc and various conditionsassociated with a gear tooth generating operation in order to maintainthe aforementioned ideal contact pattern regardless of displacement ofeither shaft and displacement of gear teeth in a highly loaded state.

According to the present invention, since the hourglass worm gear isgenerated by using a torus type grinding wheel for grinding gear toothsurfaces of which radius of curvature is represented by r=(-0.3 to 1.0)e where e designates a center distance between the worm shaft and thewheel shaft, the following advantageous effects are obtained.

(1) An effective gear tooth engagement range can be widened and a loadbearing ability can be improved substantially.

(2) An angle defined by simultaneous contact lines and the direction ofa relative speed can be enlarged and a thickness of lubricant film canbe increased. Consequently, it can be expected that an operationalefficiency of the hourglass worm gear can be improved substantially.

(3) Deterioration of a contact pattern in the load state and undesirablereduction of an effective gear tooth engagement area can be preventedreliably (it is possible to maintain 80% of a normal gear toothengagement area).

(4) It becomes possible to use a material for the worm wheel havingexcellent mechanical properties and a high strength by virtue of theadvantageous effects as mentioned in the preceding paragraphs (1) to(3), whereby a load bearing ability can be improved further.

Specifically, it becomes possible to use, e.g., a copper alloy or asteel having a hardness ranging from 200 to 300 H_(B) as a material forthe worm wheel.

In addition, an engineering plastic material may be used as a materialfor the worm wheel.

Other objects, features and advantages of the present invention willbecome apparent from reading of the following description which has beenmade in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated in the following drawings in which:

FIG. 1a is a perspective view which schematically of a worm gear and acircle S_(P) as a trace of a point on a surface S_(C) of a torus;

FIG. 1(b) is an example of a grinding wheel in the form of a torusrotatable around axis A of FIG. 1(a);

FIG. 2a is a cross sectional view of the torus of r>0 in which an outersurface of the torus is convex with a center Q of the circle of theouter surface S_(c) being positioned at the grinding wheel side;

FIG. 2(b) is a cross-sectional view of the torus of r<0 in which anouter surface of the torus is concave with a center Q of the outersurface S_(c) being positioned at the worm gear side.

FIGS. 3(A) to 3(C) are an illustrative view which shows a locus of aseries of contact lines along which the hourglass worm gear of thepresent invention shown in FIG. 1 meshes with a worm wheel,respectively;

FIGS. 4(A) to 4(D) are an illustrative view which shows variation of agear tooth engagement surface along which the hourglass worm gear of thepresent invention meshes with a worm wheel as well as variation of agear tooth engagement surface along which a prior hourglass worm gearmeshes with a worm wheel, respectively;

FIG. 5 is a perspective view of the worm gear and a circle S_(P) as atrace of a point on the surface S_(c) of the torus;

FIGS. 6(A) and 6(B) are an illustrative view which shows variation of agear tooth engagement surface along which the hourglass worm gear of thepresent invention meshes with a worm wheel, respectively, wherein FIG.6(A) shows a case where one of a worm shaft and a wheel shaft isdisplaced relative to the other one and FIG. 6 ( B ) shows a case whereno shaft displacement takes place;

FIG. 7(A) is a fragmentary view which schematically illustrates a priorhourglass worm gear produced in accordance with a method of producing ahourglass worm gear adapted to mesh with a worm wheel as disclosed in anofficial gazette of Japanese Publication Patent NO. 19970/ 1987;

FIG. 7 (B) is a fragmentary view which schematically illustrates a wormwheel meshing with the prior hourglass worm gear shown in FIG. 7(A);

FIG. 8 is a plan view which schematically illustrates arrangement of agrinding wheel for producing a prior hourglass worm gear adapted to meshwith a worm wheel by utilizing the conical surface of a conical typegrinding wheel;

FIG. 9 is a plan view which schematically illustrates a grinding wheelfor producing a prior hourglass worm wheel adapted to mesh with a wormwheel by utilizing the bottom surface of a conical type grinding wheel;and

FIG. 10 is a perspective view which schematically illustrates a PriorArt relationship among a worm shaft, a wheel shaft and an intermediategear shaft to explain an intermediate gear theory which is applicable toa case where a conventional hourglass worm gear is produced by using anintermediate gear.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Now, the present invention will be described in detail hereinafter withreference to the accompanying drawings which illustrate preferredembodiments of the present invention.

First Embodiment

An hourglass worm gear adapted to mesh with a worm wheel in accordancewith a first embodiment of the present invention will be described belowwith reference to FIG. 1 to FIG. 4.

In the drawings, A₁ designates a worm shaft, A₂ designates a wheelshaft, A₃ designates a tool shaft, A designates a grinding wheel shaft,ω₁ designates an angular speed of an hourglass worm gear, ω₂ designatesan angular speed of a worm wheel, ω₃ designates an angular speed of atool, iis designates a ratio of the angular speed of the worm gear tothe angular speed of the worm wheel (=|ω₁ |/|ω₂ |), Q designates acenter of a circular arc representing a sectional shape of a grindingwheel, S_(C) designates a circular arc representing a sectional shape ofthe grinding wheel, S_(Q) designates a locus scribed by the point Qabout the grinding wheel shaft A, r designates a radius of the circulararc S_(C) and e designates a center distance between the worm shaft A₁and the wheel shaft A₂.

Characterizing features of the hourglass worm gear of the presentinvention will be described below.

(1) The hourglass worm gear 10 is generated by using the grinding wheel12 including a torus surface to serve as a grinding surface. As shown inFIG. 1a, the tool shaft A₃ is located at the same position as that ofthe wheel shaft A₂, and a quantity of displacement of the tool relativeto the worm gear to be generated as represented by ω₃ and ω₁ coincideswith a quantity of displacement of the worm wheel relative to the wormgear as represented by ω₂ and ω₁ (Refer to FIG. 2).

(2) The worm wheel is generated by using a hob including a basic curvedsurface coincident to the worm gear tooth surface.

(3) With the hourglass worm gear as designed in the above-describedmanner, dual line contact takes place along two contact lines, i.e. , acontact line that is a primary contact line along which the worm gearfirst comes in contact with the grinding wheel (first contact line) anda contact line along which the worm gear secondarily comes in contactwith the grinding wheel (second contact line). Thus, the first locussurface and the second locus surface representing locus surfaces definedby the foregoing contact lines intersect each other along a curved linedefined by a series of points on limitative normal lines. In thisrespect, the hourglass worm gear of the present invention is basicallycoincident to the prior hourglass worm gear.

(4) The worm tooth surface is divided into two regions by the curvedline defined by a series of points on limitative normal lines, and oneof the two regions is an ineffective gear tooth surface portion. In acase where the hourglass worm gear meshes with the worm wheel at a rightangle, the aforementioned curved line intersects the commonperpendicular line to the worm shaft and the wheel shaft. Thus, thehourglass worm gear of the present invention makes it possible to locatethe foregoing intersection away from the effective gear tooth engagementregion, i.e., toward the worm shaft as far as possible so as to allowthe effective gear tooth engagement region to be widened.

(5) Design example

Referring to FIG. 1 and FIG. 2 again, the wheel shaft A2 coincides withthe tool shaft A3 that is a rotational shaft of the grinding wheel. Astraight line intersecting the worm shaft A1 and the wheel shaft A2 at aright angle is represented by L1, the intersection where the worm shaftA1 intersects the straight line L1 is represented by P1, theintersection where the wheel shaft A2 intersects the straight line L1 isrepresented by P2, the distance between the point P1 and the point P2 isrepresented by e, the point located on the straight line L1 at adistance a beyond the point P2 is represented by P3, the straight lineextending through the point P3 in parallel with the shaft A1 isrepresented by L2, the straight line derived by turning the straightline L2 about the straight line L1 by an angle δ is represented by L3which corresponds to the grinding wheel shaft A, the point located onthe straight line L3 away from the point P3 by a distance b isrepresented by P4, the straight line extending through the point P4 inparallel with the straight line L1 is represented by L4, the pointlocated on the straight line L4 away from the point P4 by a distance cis represented by P5, the straight line located on the plane inclusiveof the straight line L3 and the straight line L4 while slantwiseextending by an angle α relative to the dashed line which isperpendicular to the straight line L3 and intersect the straight line L4at the point P5 is represented by L5 and the point located on thestraight line L5 away from the point P5 by a distance r is representedby Q. With such an arrangement as mentioned above, the cross-sectionalshape of the grinding wheel exhibits a circular arc S_(C) which extendsabout the point Q. In addition, the grinding wheel includes a surface,i.e., a torus surface which is formed by turning the circular arc S_(C)about the straight line L3, and an average radius of the grinding wheelon the torus surface is represented by c. It should be added that thelocus scribed by the point Q is represented by S_(Q).

A required hourglass worm gear is produced by arranging a grinding wheelshaft A including the aforementioned torus surface in the form of arotational shaft such that the grinding wheel shaft A coincides with thestraight line L3 and then gradually turning the grinding wheel about thetool shaft A3 while rotating the grinding wheel about the grinding wheelshaft A at a high speed. At this time, rotation of the grinding wheelabout the tool shaft A3 is synchronized with rotation of a blank for therequired hourglass worm gear about the worm shaft A1 in accordance withthe intermediate gear theory as described above.

It should be noted that when the distance r is more than zero, theresultant grinding wheel surface exhibits a convex torus contour andwhen the distance r is less than zero, the resultant grinding wheelsurface exhibits a concave torus contour. As shown in FIGS. 2(a) and2(b), when the radius r is positive, the center of the circle of thecross section is positioned at the grinding wheel side and the contoursurface of the torus is convex. When the radius r is negative, thecenter is positioned at the worm gear side and the contour surface ofthe torus is concave.

When the speed reduction ratio i is set to 40, the hourglass worm gearof the present invention assumes dimensions as shown in Table 1, forexample.

                  TABLE 1                                                         ______________________________________                                        center distance between worm gear                                                                          1.0 mm                                           and worm wheel: e                                                             angle defined by worm gear shaft                                                                           90°                                       and worm wheel shaft                                                          speed reduction ratio: i     40                                               dimensions             α                                                                             20°                                       associated with        δ                                                                             12°                                       grinding wheel         a     0.20061 mm                                                              b     0.03058 mm                                                              c     1.0 mm                                           ______________________________________                                    

Next, description will be made below with reference to Table 1 as to theresults derived from analyzing a contact pattern of the grinding wheelas well as variation of gear tooth engagement appearing in a loadedstate as the radius r indicative of the circular arc of the grindingwheel varies, in comparison with those derived from the prior hourglassworm gear.

FIGS. 3(A) to (C) show a locus scribed by a plurality of contact lines(where the speed reduction ratio i is 40), respectively. When the radiusr is-0.2 mm (see FIG. 3(C)), the curve defined by a series of points onlimitative normal lines is displaced in the direction toward the wormshaft, whereby the effective gear tooth engagement range is widened.

In addition, when the radius r is-0.2 (FIG. 3(C)), the contact lineappearing in the region extending from the throat portion of the wormwheel to the end part of gear tooth engagement assumes a large anglerelative to the direction of extension of each gear tooth.

Referring to FIGS. 3(A) to (C) again, reference numerals (1) to (5) and(1)' to (5)' designate the number of each contact line, respectively.

With the conventional hourglass worm gear, it has been found that mostof the curves each defined by a series of points on limitative normallines pass from the dedendum toward the addendum in the region extendingfrom the central part of gear tooth engagement with the worm wheel tothe outlet of the same (see FIG. 7(A)). As a result, a part of the toothsurface of the worm gear becomes ineffective resulting in the gear toothengagement range being undesirably restricted. Additionally, it has beenfound that the conventional hourglass worm gear has few contact lines atthe end part of gear tooth engagement which exhibit a large anglerelative to the direction of a relative speed.

Next, the results derived from analyzing variation of gear toothengagement in a loaded state are shown in FIG. 4 with respect to thehourglass worm gear of the present invention of which gear toothdimensions are shown in Table 2.

                  TABLE 2                                                         ______________________________________                                                     A     B        C        D                                        ______________________________________                                        center distance be-                                                                              100          mm                                            tween worm gear and                                                           worm wheel                                                                    speed reduction ratio                                                                            90                                                         dimensions   a     20.061 mm      10 mm                                                                              41 mm                                  associated with                                                                            b      3.126 mm    27.3 mm                                       grinding wheel                                                                             c       100 mm                                                                r     20 mm   -20 mm                                                          δ                                                                             12°   12.5°                                  ______________________________________                                    

When it is presumed that shaft displacement takes place such that thehourglass worm gear is displaced toward the starting side of gear toothengagement relative to the worm wheel in a loaded state by a distance of50 microns in parallel with the rotational shaft located at the normalposition, and the center distance e between the worm shaft and the wheelshaft is elongated by a distance of 25 microns, about 45% of the totalnormal gear tooth engagement area is maintained as a tooth engagementregion when the radius r is 0.2 e. In contrast with the hourglass wormgear of the present invention, the conventional hourglass worm gear hasa total normal gear tooth engagement area which is smaller than 10% ofthat of the hourglass worm gear of the present invention.

In Table 2, A represents a case where the radius of the hourglass wormgear of the present invention has a non-linear circular arc tooth shapeis 0.2 e, B represents a case where the radius of the hourglass wormgear of the present invention has a non-linear circular arc tooth shapeis-0.2 e, C represents a case where the conventional hourglass worm gearas shown in FIG. 8 is used, and D represents a case where theconventional hourglass worm gear as shown in FIG. 9 is used.

Referring to FIG. 4 again, the shaded part designates a gear toothengagement portion and NO. designates the number of each worm wheel.

SECOND EMBODIMENT

Next, an hourglass worm gear in accordance with a second embodiment ofthe present invention will be described below with reference to FIG. 5and FIG. 6.

In the drawings, A1 designates a worm shaft, A2 designates a wheelshaft, A3 designates a tool shaft, A designates a grinding wheel shaft,Q designates a center of a circular arc representing a sectional shapeof a grinding wheel, S_(C) designates a circular arc representing thesectional shape of the grinding wheel, S_(Q) designates a locus scribedby the point Q about the grinding wheel Shaft A, r designates a radiusof the circular arc Q_(C), R designates a radius of rotation of thepoint Q, δ designates an inclination angle of the grinding wheel ShaftA, e₁ designates a quantity of offsetting of the grinding wheel Shaft A,b designates a quantity of offsetting of the radius of R of the point Qat the foot part of the same, e designates a center distance between theworm shaft A1 and the wheel shaft A2, φ₁ designates an angle of rotationof the worm gear, ω₁ designates an angular speed of the worm gear, φ₂designates an angle of rotation of the worm wheel, ω₂ designates anangular speed of the worm wheel, φ₃ designates an angle of rotation ofthe tool, ω₃ designates an angular speed of the tool is a ratio of theangular speed of the worm gear to the angular speed of the worm wheel,i.e., ω₁ /ω₂, wherein φ₁ is represented by φ₁ =f₃₁ φ₃ +f₃₂ φ₂ +f₃₃ φ₃.

According to the second embodiment, a series of gear tooth surfaces onthe hourglass worm gear are successively generated by using a grindingwheel including a torus surface in the form of a circular arc as agrinding wheel surface as viewed in a cross-sectional plane in the samemanner as the first embodiment of the present invention.

To perform a worm gear tooth generating operation, a system of machininga blank for the hourglass worm gear in a shifted state at a differentspeed wherein a ratio of the number of revolutions of a tool shaft tothe number of revolutions of a shaft of a blank for the worm gear to bemachined and a center distance between the worm shaft and the wheelshaft are changed from those specified based on given gear dimensions,during the worm gear tooth surface generating operation is employed forpracticing the second embodiment of the present invention.

In addition, a series of gear tooth surfaces on the hourglass worm gearare successively generated by continuously changing the ratio of thenumber of revolutions of the worm shaft to the number of revolutions ofthe tool shaft during the worm gear tooth surface generating operation.

Referring to FIG. 5 and FIG. 6 again, it is assumed that the straightline intersecting the worm shaft A1 and the wheel shaft A2 at a rightangle is represented by L1, the intersection where the worm shaft A1intersects the straight line L1 is represented by P1, the intersectionwhere the wheel shaft A2 intersects the straight line L1 is representedby P2, the distance between the point P1 and the point P2 is representedby e, the point located on an extension extending from the straight lineL1 in the direction toward the point P2 is represented by P3, thedistance between the point P1 and the point P3 is represented by e_(C),the tool shaft extending through the point P3 in parallel with the wheelshaft A2 is represented by A3, the point located on the tool shaft A3away from the point P3 by a distance of e₁ is represented by P4, thestraight line extending through the point P4 in parallel with the wormshaft A1 is represented by L2, the straight line derived by turning thestraight line L2 about the point P3 by an angle δ in a plane inclusiveof the tool shaft A3 is represented by L3 which corresponds to thegrinding wheel shaft A, the point located on the straight line L3 awayfrom the point P4 by a distance of b₂ is represented by P5, the pointlocated at the position away from the point P5 by a distance of R in aperpendicular plane relative to the straight line L3 extending throughthe point P5 is represented by Q and the circular arc having a radius rwith the point Q as a center in the foregoing perpendicular plane isrepresented by S_(C). With such arrangement as mentioned above, agrinding wheel surface is formed on the torus surface which has beenformed by turning the circular arc S_(C) about the straight line L3. Itshould be noted that when the radius r is more than zero, the resultantgrinding wheel surface exhibits a convex torus contour and when theradius r is less than zero, the resultant grinding wheel surfaceexhibits a concave torus contour.

A required hourglass worm gear is produced by arranging a grinding wheelshaft A, i.e., a rotational shaft of the grinding wheel including atorus surface such that the grinding wheel shaft A coincides with thestraight line L3 and then gradually turning the grinding wheel about thetool shaft A3 while rotating the grinding wheel about the grinding wheelshaft A at a high speed. At this time, rotation of the grinding wheelabout the tool shaft A3 is synchronized with rotation of a blank for theworm gear about the worm shaft A1 in accordance with gear generatingtheory.

A series of gear tooth surfaces on the worm wheel are successivelygenerated based on the same center distance and rotational ratio asthose specified by given gear dimensions, by using a hob including thesame curved surface as that of the gear tooth surfaces on the worm gearas a basic curved surface (see FIG. 5).

Gear tooth dimensions and gear tooth generating dimensions employed forpracticing the second embodiment of the present invention are as shownin Table 3.

                  TABLE 3                                                         ______________________________________                                                       II - A    II - B                                               ______________________________________                                        center distance between worm                                                                   100 mm                                                       gear and worm wheel                                                           angle between worm gear shaft                                                                  90°                                                   and worm wheel shaft                                                          speed reduction ratio                                                                          40.sup.                                                      gear tooth cutting                                                                           e.sub.C                                                                             127.7    mm   104    mm                                  dimensions     f.sub.31                                                                            53.85         42                                                        f.sub.32                                                                            -2.6502       -0.46221                                                  f.sub.33                                                                            1.1739        0                                                         r     70       mm   60     mm                                                 R     80       mm   80     mm                                                 δ                                                                             1°35'2"                                                                              1°7'54"                                            e.sub.1                                                                             37.308   mm   37.126 mm                                                 b     8.031    mm   10.591 mm                                  ______________________________________                                    

The results derived from analyzing gear tooth engagement with thehourglass worm gear in accordance with the second embodiment of thepresent invention under conditions that the worm gear is displacedtoward the gear tooth engagement starting side by a distance of 50microns relative to the worm wheel in a loaded state and the worm gearis displaced further by a distance of 25 microns in the direction ofelongation of the center distance are shown in FIG. 6 together withthose derived in a case where no displacement takes place (with normalgear tooth engagement maintained).

As is apparent from FIG. 6, according to the second embodiment of thepresent invention, an effective gear tooth engagement area of 70 to 80%can be obtained. In the drawing, the shaded part designates a gear toothengagement portion and NO. designates the number of each gear tooth onthe worm wheel.

As will be apparent from the above analysis, the hourglass worm geartooth generated in accordance with the aforementioned gear cuttingprinciple makes it possible to make adjustment such that a group ofprojections derived from projecting a group of normal lines relative tocontact points on each gear tooth surface onto the plane relative to theworm wheel shaft pass through the center of rotation of the circular arcof the grinding wheel during displacement of either shaft in a loadedstate or pass through a narrow region in the vicinity of the center ofrotation of the same, resulting in undesirable reduction of an effectivegear tooth engagement area in the loaded state being prevented reliably.

Since the hourglass worm gear of the present invention assures that apressure on the gear tooth surface can substantially be reduced to alevel of about 1/5 in contrast with the conventional hourglass wormgear, an engineering plastic material (e.g., MC nylon) can be employedas a material for the worm wheel, provided that the hourglass worm gearis dimensioned to have the same size as that of the conventionalhourglass worm gear. Consequently, the following advantageous effectscan be expected with the hourglass worm gear of the present invention.

(a) It becomes possible to use an assembly of the hourglass worm gearand the worm wheel without any lubricant.

(b) Generation of noisy sound can be reduced substantially (e.g., 70dB(A) of the conventional hourglass worm gear can be reduced to a levelof 45 dB(A) with the hourglass worm gear of the present invention).

(c) Weight of the assembly of the hourglass worm gear and the worm wheelcan be reduced to a level of 1/7 compared with an assembly of theconventional hourglass worm gear and the opponent worm wheel.

(d) A production cost can be reduced to a level of 1/2 compared with theconventional hourglass worm gear.

While the present invention has been described above with respect to thetwo preferred embodiments thereof, it should of course be understoodthat the present invention should not be limited only to theseembodiments but various changes or modifications may be made withoutdeparture from the scope of the invention as defined by the appendedclaims.

We claim:
 1. An apparatus for making an hourglass worm gear for meshingwith a worm wheel comprising:a worm shaft provided in connection withsaid worm gear; a wheel shaft provided in connection with said wormwheel; a grinding wheel for grinding gear tooth surfaces in said wormgear, said grinding wheel having a radius of curvature of an arc-shapedcross-sectional contour represented by "r"; said worm shaft and saidwheel shaft having a distance therebetween represented by "e"; and meansfor successively generating a series of gear tooth surfaces in said wormgear with said grinding wheel such that r=(-0.3 to 1.0)e, wherein aneffective gear tooth engagement range is enlarged and a load bearingability is increased.
 2. The hourglass worm gear according to claim 1,wherein said grinding wheel includes a torus surface.